Comptes Rendus
Evolution of functional connectivity in contact and force chain networks: Feature vectors, k-cores and minimal cycles
Comptes Rendus. Mécanique, Micromechanics of granular materials, Volume 338 (2010) no. 10-11, pp. 556-569.

We analyze the rheological response, i.e., fabric and contact force evolution, of dense granular materials from a complex networks perspective. The strain evolution of three classes of subnetworks, i.e., k-cores, minimal cycles and force chain networks, elucidates the breakdown of functional connectivity and structure in the lead up to and during failure. Feature vectors and dynamics occurring in such networks in three different biaxially compressed two-dimensional samples reveal some common aspects which are suggestive of an intrinsic structural hierarchy in granular networks – while differences shed light on the influence of confining pressure and interparticle rolling resistance on the evolution of these networks both at the mesoscopic as well as macroscopic levels.

Nous analysons la réponse constitutive de matériaux granulaires denses, au travers de l'évolution des forces de contact et de la texture, dans le cadre des réseaux complexes. L'évolution des déformations de trois classes de sous-réseaux, comprenant les cycles minimaux et les chaines de force, permet d'éclairer la disparition de connectivité fonctionnelle et de structure au cours du processus de rupture. L'analyse des processus dynamiques associés à de tels réseaux, au sein d'échantillons comprimés de manière biaxiale, révèle des aspects communs qui suggèrent l'existence d'une hiérarchie structurelle intrinsèque. En outre, l'influence de la pression de confinement et de la résistance au roulement inter-particulaire sur l'évolution de tels réseaux apparaît clairement aux échelles mésoscopique et macroscopique.

Published online:
DOI: 10.1016/j.crme.2010.09.004
Keywords: Rheology, Granular materials
Mots-clés : Rhéologie, Matériaux granulaires

Antoinette Tordesillas 1; Patrick O'Sullivan 1; David M. Walker 1; Paramitha 1

1 Department of Mathematics & Statistics, University of Melbourne, Parkville, Victoria 3010, Australia
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Antoinette Tordesillas; Patrick O'Sullivan; David M. Walker; Paramitha. Evolution of functional connectivity in contact and force chain networks: Feature vectors, k-cores and minimal cycles. Comptes Rendus. Mécanique, Micromechanics of granular materials, Volume 338 (2010) no. 10-11, pp. 556-569. doi : 10.1016/j.crme.2010.09.004. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2010.09.004/

[1] J.P. Bardet; J. Proubet The structure of shear bands in idealized granular materials, Applied Mechanics Reviews, ASME, Volume 45 (1992), p. S118-S122

[2] K. Iwashita; M. Oda Micro-deformation mechanism of shear banding process based on modified distinct element method, Powder Technology, Volume 109 (2000), pp. 192-205

[3] D.A. Horner; J.F. Peters; A.J. Carrillo Large scale discrete element modeling of vehicle–soil interaction, Journal of Engineering Mechanics, Volume 127 (2001), pp. 1027-1032

[4] P.A. Cundall A discontinuous future for numerical modeling in soil and rock, ASCE Conference Proceedings, Volume 259 (2002), p. 1 | DOI

[5] S.J. Antony; M.R. Kuhn Influence of particle shape on granular contact signatures and shear strength: New insights from simulations, International Journal of Solids and Structures, Volume 41 (2004), pp. 5863-5870

[6] L. Rothenburg; N.P. Kruyt Critical state and evolution of coordination number in simulated granular materials, International Journal of Solids and Structures, Volume 41 (2004), pp. 5763-5774

[7] C. Thornton; L. Zhang A numerical examination of shear banding and simple shear non-coaxial flow rules, Philosophical Magazine, Volume 86 (2006), pp. 3425-3452

[8] F. Alonso-Marroquin; S. Luding; H.J. Herrmann; I. Vardoulakis Role of anisotropy in the elastoplastic response of a polygonal packing, Physical Review E, Volume 71 (2006), p. 051304

[9] C. Salot; P. Gotteland; P. Villard Influence of relative density on granular materials behavior: DEM simulations of triaxial tests, Granular Matter, Volume 11 (2009), pp. 221-236

[10] T. Matsushima; J. Katagiri; K. Uesugi; A. Tsuchiyama; T. Nakano 3D shape characterization and image-based DEM simulation of the lunar soil simulant FJS-1, Journal of Aerospace Engineering, Volume 22 (2009), pp. 15-23

[11] P.A. Cundall; O.D.L. Strack A discrete numerical model for granular assemblies, Geotechnique, Volume 29 (1979), pp. 47-65

[12] M. Oda; K. Iwashita Mechanics of Granular Materials: An Introduction, A.A. Balkema, Brookfield, VT, 1999

[13] I. Aranson; L. Tsimring Granular Patterns, Oxford University Press, 2009

[14] Mechanics of Granular Materials: An Introduction (M. Oda; K. Iwashita, eds.), A.A. Balkema, Rotterdam, 1999

[15] J.S. Andrade; H.J. Herrmann; R.F.S. Andrade; L.R. Da Silva Apollonian networks: Simultaneously scale-free, small world, Euclidean, space filling and with matching graphs, Physical Review Letters, Volume 94 (2005), p. 018702

[16] A. Smart; J.M. Ottino Granular matter and networks: Three related examples, Soft Matter, Volume 4 (2008), pp. 2125-2131

[17] A. Smart; J.M. Ottino Evolving loop structure in gradually tilted two-dimensional granular packings, Physical Review E, Volume 77 (2008), p. 041307

[18] A.A. Peña; H.J. Hermann; P.G. Lind Force chains in sheared granular media of irregular particles (M. Nakagawa; S. Luding, eds.), Powders & Grains 2009, Proceedings of the 6th International Conference Micromechanics of Granular Media 2009, AIP Conference Proceedings, vol. 1145, AIP, Colorado, USA, 2009

[19] D.M. Walker; A. Tordesillas Topological evolution in dense granular materials: A complex networks perspective, International Journal of Solids and Structures, Volume 47 (2010), pp. 624-639

[20] S.H. Strogatz Exploring complex networks, Nature, Volume 410 (2001), pp. 268-276

[21] R. Albert; A.-L. Barabási Statistical mechanics of complex networks, Reviews of Modern Physics, Volume 74 (2002), pp. 47-97

[22] E. Estrada; J.A. Rodríguez-Velázquez Subgraph centrality in complex networks, Physical Review E, Volume 71 (2005), p. 056103

[23] E. Estrada; J.A. Rodríguez-Velázquez Spectral measures of bipartivity in complex networks, Physical Review E, Volume 72 (2005), p. 046105

[24] P.G. Lind; M.C. González; H.J. Herrmann Cycles and clustering in bipartite networks, Physical Review E, Volume 72 (2005), p. 056127

[25] L. da F. Costa; F.A. Rodrigues; G. Travieso; P.R. Villas Boas Characterization of complex networks: A survey of measurements, Advances in Physics, Volume 56 (2007), pp. 167-242

[26] A. Tordesillas; D.M. Walker; Q. Lin Force chains and force cycles, Physical Review E, Volume 81 (2010), p. 011302

[27] A. Tordesillas, Q. Lin, J. Zhang, R.P. Behringer, J.Y. Shi, Structural stability of self-organized cluster conformations in dense granular materials, 2010, in preparation.

[28] A. Tordesillas, D.M. Walker, G. Froyland, R.P. Behringer, J. Zhang, Structural stability and transition dynamics of granular motifs, unpublished manuscript, 2010.

[29] S. Boccaletti; V. Latora; Y. Moreno; M. Chavez; D.-U. Hwang Complex networks: Structure and dynamics, Physics Reports, Volume 424 (2006), pp. 175-308

[30] A. Drescher; G. de Josselin de Jong Photoelastic verification of a mechanical model for the flow of a granular material, Journal of the Mechanics and Physics of Solids, Volume 20 (1972), pp. 337-340

[31] A. Tordesillas; J. Zhang; R.P. Behringer Buckling force chains in dense granular assemblies: Physical and numerical experiments, Geomechanics and Geoengineering, Volume 4 (2009), pp. 3-16

[32] J. Zhang; T.S. Majmudar; A. Tordesillas; R.P. Behringer Statistical properties of a 2D granular materials subjected to cyclic shear, Granular Matter, Volume 12 (2010), pp. 159-172

[33] F. Radjai; D. Wolf; M. Jean; J. Moreau Bimodal character of stress transmission in granular packings, Phys. Rev. Lett., Volume 80 (1998), pp. 61-64

[34] S.N. Dorogovtsev; A.V. Goltsev; J.F.F. Mendes k-core organization of complex networks, Physical Review Letters, Volume 96 (2006), p. 040601

[35] A. Tordesillas Force chain buckling, unjamming transitions and shear banding in dense granular assemblies, Philosophical Magazine, Volume 87 (2007), pp. 4987-5016

[36] M. Muthuswamy; A. Tordesillas How do interparticle contact friction, packing density and degree of polydispersity affect force propagation in particulate assemblies?, Journal of Statistical Mechanics: Theory and Experiment (2006), p. P09003

[37] S.J. Antony Link between single-particle properties and macroscopic properties in particulate assemblies: Role of structures within structures, Philosophical Transactions of The Royal Society A, Volume 365 (2007), pp. 2879-2891

[38] C. Thornton; L. Zhang A numerical examination of shear banding and simple shear non-coaxial flow rules, Philosophical Magazine, Volume 86 (2006), pp. 3425-3452

[39] T.-T. Ng Macro- and micro-behaviors of granular materials under different sample preparations methods and stress paths, International Journal of Solids and Structures, Volume 41 (2004), pp. 5871-5884

[40] M.R. Kuhn; K. Bagi Contact rolling and deformation in granular media, International Journal of Solids and Structures, Volume 41 (2004), pp. 5793-5820

[41] K. Iwashita; M. Oda Rolling resistance at contacts in simulation of shear band development by DEM, ASCE Journal of Engineering Mechanics, Volume 124 (1998), pp. 285-292

[42] A. Tordesillas; M. Muthuswamy On the modeling of confined buckling of force chains, Journal of the Mechanics and Physics of Solids, Volume 57 (2009), pp. 706-727

[43] D. Volfson; L.S. Tsimring; I.S. Aranson Stick-slip dynamics of a granular layer under shear, Physical Review E, Volume 69 (2004), p. 031302

[44] F. Dalton; D. Corcoran Self-organized criticality in a sheared granular stick-slip system, Physical Review E, Volume 63 (2001), p. 061312

[45] A. Tordesillas; M. Muthuswamy; S.D.C. Walsh Mesoscale measures of nonaffine deformation in dense granular assemblies, ASCE Journal of Engineering Mechanics, Volume 134 (2008), pp. 1095-1113

[46] R.E. Tarjan Depth first search and linear graph algorithms, SIAM Journal on Computing, Volume 1 (1972), pp. 146-160

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